Bài tập cuối chương I. ỨNG DỤNG ĐẠO HÀM

Home Lớp 12 Toán lớp 12 - Sách Kết nối tri thức Bài tập cuối chương I. ỨNG DỤNG ĐẠO HÀM ĐỂ KHẢO SÁT VÀ VẼ ĐỒ THỊ HÀM SỐ.Bài tập trung bình

{"common":{"save":0,"post_id":"7550","level":2,"total":10,"point":10,"point_extra":0},"segment":[{"id":"5529","post_id":"7550","mon_id":"1159285","chapter_id":"1159288","question":"Cho hàm s\u1ed1 $y = f(x)$<\/span> xác \u0111\u1ecbnh trên \u211d và có \u0111\u1ea1o hàm $f^\\prime(x)=x(x-1)^2(x-2)$<\/span>. Hàm s\u1ed1 $y = f(x)$<\/span> có bao nhiêu \u0111i\u1ec3m c\u1ef1c<\/p>tr\u1ecb?<\/p>","options":["A.<\/strong> 0","B.<\/strong> 1","C.<\/strong> 2","D.<\/strong> 3"],"correct":"3","level":"2","hint":"S\u1eed d\u1ee5ng \u0111\u1ecbnh ngh\u0129a c\u1ef1c tr\u1ecb c\u1ee7a hàm s\u1ed1.<\/p>","answer":"Ch\u1ecdn C.<\/strong> 2<\/span><\/p>Ta có: $f^\\prime(x)=x(x-1)^2(x-2)=0$<\/span> ⇔ x = 0 ho\u1eb7c x = 1 ho\u1eb7c x = 2.<\/p>Qua x = 1, \u0111\u1ea1o hàm c\u1ee7a hàm s\u1ed1 không \u0111\u1ed5i d\u1ea5u, nên hàm s\u1ed1 ch\u1ec9 có 2 \u0111i\u1ec3m c\u1ef1c tr\u1ecb.<\/p>","type":"choose","extra_type":"shape2","user_id":"131","test":"0","date":"2024-08-25 04:34:30","option_type":"txt","len":0},{"id":"5530","post_id":"7550","mon_id":"1159285","chapter_id":"1159288","question":"T\u1ed5ng các giá tr\u1ecb nguyên c\u1ee7a tham s\u1ed1 m trong \u0111o\u1ea1n [–10; 10] \u0111\u1ec3 hàm s\u1ed1 $y=\\dfrac{1}{3}x^3+2x^2-mx-1$<\/span> \u0111\u1ed3ng bi\u1ebfn trên \u211d b\u1eb1ng bao nhiêu?<\/p>","options":["A.<\/strong> 49","B.<\/strong> –49","C.<\/strong> –45","D.<\/strong> 45"],"correct":"2","level":"2","hint":"S\u1eed d\u1ee5ng \u0111\u1ecbnh ngh\u0129a \u0111\u1ed3ng bi\u1ebfn c\u1ee7a hàm s\u1ed1.<\/p>","answer":"Ch\u1ecdn B.<\/strong> –49<\/span><\/p>Ta có: $y^\\prime=x^2+4x-m$<\/span>.<\/p>\u0110\u1ec3 hàm s\u1ed1 \u0111\u1ed3ng bi\u1ebfn trên \u211d thì $y^\\prime\\ge0,\\forall x\\in $<\/span> \u211d ⇔ $\\begin{cases}a>0\\\\\\Delta^\\prime\\le0\\end{cases}$<\/span> ⇔ $\\begin{cases}1>0\\\\4+m\\le0\\end{cases}$<\/span> ⇔ $m\\le-4$<\/span>.<\/p>Vì m ∈ [–10; 10] và m ∈ \u2124 nên m ∈ {–10; –9; –8; –7; –6; –5; –4}.<\/p>Do \u0111ó t\u1ed5ng các giá tr\u1ecb c\u1ee7a m b\u1eb1ng <\/p>$(-10)+(-9)+(-8)+(-7)+(-6)+(-5)+(-4)=-49$<\/span><\/p>","type":"choose","extra_type":"shape1","user_id":"131","test":"0","date":"2024-08-25 04:41:34","option_type":"txt","len":0},{"id":"5532","post_id":"7550","mon_id":"1159285","chapter_id":"1159288","question":"Cho hàm s\u1ed1 $y=f(x)$<\/span> có b\u1ea3ng bi\u1ebfn thiên nh\u01b0 sau:<\/p><svg height=\"150\" width=\"400\"> <g><title><\/title><rect fill=\"#d4ffaa\" height=\"152\" id=\"canvas_background\" width=\"402\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" id=\"canvasGrid\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" id=\"svg_19\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g><title><\/title><line fill=\"none\" id=\"svg_1\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"-3.13637\" x2=\"399.86362\" y1=\"26.43181\" y2=\"26\"><\/line> <line fill=\"none\" id=\"svg_2\" stroke=\"#000\" 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text-anchor=\"start\" x=\"6.86363\" xml:space=\"preserve\" y=\"99.43181\">f(x)<\/text> <g id=\"svg_9\"> <text fill=\"#000000\" font-family=\"Times New Roman, Times, serif\" font-size=\"20\" id=\"svg_7\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"370.86363\" xml:space=\"preserve\" y=\"20.43181\">+<\/text> <text fill=\"#000000\" font-family=\"Times New Roman, Times, serif\" font-size=\"20\" id=\"svg_8\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(-90 390.86364746093756,14.522720336914036) \" x=\"385.86363\" xml:space=\"preserve\" y=\"21.43181\">8<\/text> <\/g> <g id=\"svg_12\"> <text fill=\"#000000\" font-family=\"Times New Roman, Times, serif\" font-size=\"20\" id=\"svg_10\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"43.86363\" xml:space=\"preserve\" y=\"71.43181\">+<\/text> <text fill=\"#000000\" font-family=\"Times New Roman, Times, serif\" font-size=\"20\" id=\"svg_11\" stroke=\"#000\" stroke-width=\"0\" 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stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" transform=\"matrix(1.8499138520500709,0,0,1,-75.69875102668512,0) \" x=\"198.78296\" xml:space=\"preserve\" y=\"140.43181\">-<\/text> <text fill=\"#000000\" font-family=\"Times New Roman, Times, serif\" font-size=\"20\" id=\"svg_34\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"300.86363\" xml:space=\"preserve\" y=\"141.43181\">2<\/text> <\/g> <text fill=\"#000000\" font-family=\"Times New Roman, Times, serif\" font-size=\"20\" id=\"svg_24\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"130.86363\" xml:space=\"preserve\" y=\"48.43181\">0<\/text> <text fill=\"#000000\" font-family=\"Times New Roman, Times, serif\" font-size=\"20\" id=\"svg_36\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"207.86363\" xml:space=\"preserve\" y=\"48.43181\">0<\/text> <text fill=\"#000000\" font-family=\"Times New Roman, Times, serif\" font-size=\"20\" id=\"svg_37\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"294.86363\" xml:space=\"preserve\" y=\"48.43181\">0<\/text> <text fill=\"#000000\" font-family=\"Times New Roman, Times, serif\" font-size=\"20\" id=\"svg_38\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"170.86363\" xml:space=\"preserve\" y=\"46.43181\">+<\/text> <text fill=\"#000000\" font-family=\"Times New Roman, Times, serif\" font-size=\"20\" id=\"svg_39\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"332.86362\" xml:space=\"preserve\" y=\"45.43181\">+<\/text> <g id=\"svg_42\" transform=\"rotate(42.36695861816406 91.37500000000003,105.06817626953125) \"> <line fill=\"none\" id=\"svg_40\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"50.86363\" x2=\"128.86363\" y1=\"105\" y2=\"105\"><\/line> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_41\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"117.86363\" xml:space=\"preserve\" y=\"113.43181\">><\/text> <\/g> <g id=\"svg_45\" transform=\"rotate(42.36695861816406 253.37500000000006,107.06817626953125) \"> <line fill=\"none\" id=\"svg_43\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"212.86363\" x2=\"290.86363\" y1=\"107\" y2=\"107\"><\/line> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_44\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"279.86363\" xml:space=\"preserve\" y=\"115.43181\">><\/text> <\/g> <g id=\"svg_48\" transform=\"rotate(-47.104148864746094 179.37498474121094,103.06817626953124) \"> <line fill=\"none\" id=\"svg_46\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"138.86363\" x2=\"216.86363\" y1=\"103\" y2=\"103\"><\/line> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_47\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"205.86363\" xml:space=\"preserve\" y=\"111.43181\">><\/text> <\/g> <g id=\"svg_51\" transform=\"rotate(-47.104148864746094 343.37500000000006,104.06817626953122) \"> <line fill=\"none\" id=\"svg_49\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"302.86363\" x2=\"380.86363\" y1=\"104\" y2=\"104\"><\/line> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_50\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"369.86363\" xml:space=\"preserve\" y=\"112.43181\">><\/text> <\/g> <\/g> <\/svg><\/span><\/p>Có bao nhiêu giá tr\u1ecb nguyên c\u1ee7a m \u0111\u1ec3 ph\u01b0\u01a1ng trình $4f(x)+m=0$<\/span> có 4 nghi\u1ec7m th\u1ef1c phân bi\u1ec7t?<\/p>","options":["A.<\/strong> 11","B.<\/strong> 0","C.<\/strong> 2","D.<\/strong> 9"],"correct":"1","level":"2","hint":"S\u1eed d\u1ee5ng s\u1ef1 t\u01b0\u01a1ng giao c\u1ee7a \u0111\u1ed3 th\u1ecb hàm s\u1ed1.<\/p>","answer":"Ch\u1ecdn A.<\/strong> 11<\/span><\/p>Ta có: $4f(x)+m=0$<\/span> ⇔ $f(x)=-\\dfrac{m}{4}$<\/span>.<\/p>Nh\u1eadn xét: s\u1ed1 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng trình \u0111ã cho chính là s\u1ed1 giao \u0111i\u1ec3m c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng $y=-\\dfrac{m}{4}$<\/span> v\u1edbi \u0111\u1ed3 th\u1ecb hàm s\u1ed1 $y=f(x)$<\/span>.<\/p>Do \u0111ó, ph\u01b0\u01a1ng trình $4f(x)+m=0$<\/span> có 4 nghi\u1ec7m th\u1ef1c phân bi\u1ec7t <\/p>⇔ $-2 < -\\dfrac{m}{4} < 1$<\/span> ⇔ –4 < m < 8.<\/p>V\u1eady m ∈ {–3; –2; –1; 0; 1; 2; 3; 4; 5; 6; 7}.<\/p>","type":"choose","extra_type":"shape1","user_id":"131","test":"0","date":"2024-08-25 04:47:15","option_type":"txt","len":0}]}